<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We present in this paper a survey of recent results on the controllability of the parabolic system governed by bilinear control. We first discuss the problem of global controllability which corresponds to the question of whether the solution of the system can be driven to a given state at a some finite time by means of a control. We give some results on the global controllability of bilinear and semilinear reaction-diffusion equations. After this we introduce the case of partial controllability with the control acting on a subregion of the domain. Illustrative examples are also provided.</p></abstract>

We present in this paper a survey of recent results on the controllability of the parabolic system governed by bilinear control. We first discuss the problem of global controllability which corresponds to the question of whether the solution of the system can be driven to a given state at a some finite time by means of a control. We give some results on the global controllability of bilinear and semilinear reaction-diffusion equations. After this we introduce the case of partial controllability with the control acting on a subregion of the domain. Illustrative examples are also provided.

Controllability of some bilinear and semilinear parabolic problems

FSDM, University of Sidi Mohamed Ben Abdellah,

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Controllability of some bilinear and semilinear parabolic problems"}

We present in this paper a survey of recent results on the controllability of the parabolic system governed by bilinear control. We first discuss the problem...

Controllability of some bilinear and semilinear parabolic problems

Published Online: Jan 24, 2020

Page range: 222 - 234

Received: Oct 10, 2019

Accepted: Dec 15, 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0016

Keywords
Parabolic system, Bilinear control, Partial controllability, Exact controllability, Semilinear system

© 2019 M. Jidou Khayar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Controllability of some bilinear and semilinear parabolic problems

Published Online: Jan 24, 2020

Page range: 222 - 234

Received: Oct 10, 2019

Accepted: Dec 15, 2019

DOI: https://doi.org/10.2478/mjpaa-2019-0016

KeywordsParabolic system, Bilinear control, Partial controllability, Exact controllability, Semilinear system

© 2019 M. Jidou Khayar, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Parabolic system, Bilinear control, Partial controllability, Exact controllability, Semilinear system